Knotting of algebraic curves in complex surfaces (Q2719824)

The author proves the following result:NEWLINENEWLINENEWLINEFor any \(d\geq 5\) there exist infinitely many smooth oriented closed surfaces \(F\) in \(\mathbb C \mathbb P^2\) representing the class \(d\in H_2(\mathbb C \mathbb P^2)=\mathbb Z\), having genus \(1/2(d-1)(d-2)\) and such that \(\pi_1(\mathbb C \mathbb P^2\setminus F)\) is isomorphic to \(\mathbb Z/d\). The pairs \((\mathbb C \mathbb P^2 ,F)\) are pairwise smoothly non-equivalent.NEWLINENEWLINENEWLINEThis theorem answers Problem 4.110 from Kirby's Problem List [Problems in low-dimensional topology. Edited by Rob Kirby. AMS/IP Stud. Adv. Math. 2 (pt. 2), 35-473 (1997; Zbl 0888.57014))]. In his previous paper [Topology 41, No. 1, 47-55 (2002)] the author proved a weak version of the result on hand, namely, for \(d\) even and \(d\geq 6\).